# Generators, relations, and homology for Ozsv\'ath-Szab\'o's Kauffman-states algebras

## TL;DR

This paper provides a detailed generators-and-relations presentation of Ozsváth-Szabó's Kauffman-states algebras, computes their homology, and investigates their formality, advancing the algebraic understanding of knot Floer homology.

## Contribution

It offers a new algebraic description and homological analysis of Ozsváth-Szabó's algebras, which were previously defined abstractly.

## Key findings

- Explicit generators-and-relations description of the algebras
- Homology computations for these algebras
- Criteria for their formality

## Abstract

We give a generators-and-relations description of differential graded algebras recently introduced by Ozsv\'ath and Szab\'o for the computation of knot Floer homology. We also compute the homology of these algebras and determine when they are formal.